document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205195>Question 1205195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the answer to this elimination equation<BR>\n" );
document.write( "-4x+2y=8<BR>\n" );
document.write( "8x-4y=-16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841844 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given system<BR>\n" );
document.write( "-4x+2y=8<BR>\n" );
document.write( "8x-4y=-16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Double both sides of the 1st equation to end up with -8x+4y=16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the given system is equivalent to this system<BR>\n" );
document.write( "-8x+4y=16<BR>\n" );
document.write( "8x-4y=-16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add straight down.<BR>\n" );
document.write( "The x's cancel.<BR>\n" );
document.write( "The y's cancel.<BR>\n" );
document.write( "The right hand sides add to 0.<BR>\n" );
document.write( "We end up with 0x+0y = 0 or simply 0 = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The equation 0 = 0 is always true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=red>There are infinitely solutions</font>. <BR>\n" );
document.write( "Each solution is of the form (x,y) where y = 2x+4<BR>\n" );
document.write( "y = 2x+4 is what happens when you solve for y in any of the equations mentioned.<BR>\n" );
document.write( "We could say that each solution is of the form (x, 2x+4) to avoid involving another variable.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If x = 0, then we get (x, 2x+4) = (0, 2*0+4) = (0, 4)<BR>\n" );
document.write( "If x = 1, then we get (x, 2x+4) = (1, 2*1+4) = (1, 6)<BR>\n" );
document.write( "If x = 2, then we get (x, 2x+4) = (2, 2*2+4) = (2, 8)<BR>\n" );
document.write( "If x = 3, then we get (x, 2x+4) = (3, 2*3+4) = (3, 10)<BR>\n" );
document.write( "and so on.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you used a tool like <a  rel=nofollow HREF=\"https://www.desmos.com/calculator\">Desmos</a> or <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> to graph, then you should notice that the two original equations produce the exact same line. Click one equation to turn it off, then click it back on, repeating this process to see the line blink. It should help show the overlap. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you prefer something like a TI83, then stick to that.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );